Definition:Normal Extension/Definition 2

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Definition

Let $L / K$ be a field extension.

Let $\overline K$ be the algebraic closure of $K$.

Let $\Gal {L / K}$ denote the set of embeddings of $L$ in $\overline K$ which fix $K$ pointwise.


Then $L / K$ is a normal extension if and only if:

$\map \sigma L = L$

for each $\sigma \in \Gal {L / K}$.


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